GCSE / IGCSE Maths – Statistics

Here are the numbers of emails received by 8 people in one day: $3,\ 7,\ 7,\ 8,\ 10,\ 12,\ 15,\ 18$.Find (a) the mean, (b) the median, (c) the mode, (d) the range.

The table shows the number of goals scored by a team in 25 matches: 0 goals (5 matches), 1 goal (8 matches), 2 goals (6 matches), 3 goals (4 matches), 4 goals (2 matches).(a) Write down the mode.(b) Find the median.(c) Calculate the mean number of goals per match.

The heights, $h$ cm, of 30 plants are grouped: $140 < h \leq 150$ (4 plants), $150 < h \leq 160$ (11), $160 < h \leq 170$ (9), $170 < h \leq 180$ (6).(a) Write down the modal class.(b) Calculate an estimate for the mean height.(c) Explain why your answer to (b) is only an estimate.

The mean of five numbers is 9. Four of the numbers are $6,\ 11,\ 4$ and $13$. Find the fifth number.

Class A has 12 students with a mean test mark of 64. Class B has 18 students with a mean test mark of 59. Calculate the mean mark of all 30 students.

The ages of members of a club are grouped: $10 < a \leq 20$ (8 members), $20 < a \leq 30$ ($x$ members), $30 < a \leq 40$ (5 members).The estimated mean age is 24 years. Find the value of $x$.

60 students were timed completing a puzzle. Times $t$ (minutes): $0 < t \leq 10$ (6 students), $10 < t \leq 20$ (14), $20 < t \leq 30$ (22), $30 < t \leq 40$ (12), $40 < t \leq 50$ (6).(a) Complete the cumulative frequency table.(b) Describe how you would draw the cumulative frequency graph (which points to plot).(c) Use linear interpolation (or a cumulative frequency graph) to estimate the median and the interquartile range.

Two groups of students sat the same test. Group A: median 38, interquartile range 14. Group B: median 45, interquartile range 9.Make two comparisons between the marks of the two groups.

The table shows the masses, $m$ kg, of 60 parcels: $0 < m \leq 5$ (frequency 10), $5 < m \leq 15$ (30), $15 < m \leq 20$ (8), $20 < m \leq 40$ (12).(a) Calculate the frequency density of each class.(b) Use the histogram to estimate the number of parcels with mass between 10 kg and 25 kg.

On a histogram, the bar for the class $20 < x \leq 30$ has a frequency density of 1.4.(a) Find the frequency of this class.(b) The class $30 < x \leq 50$ has a frequency of 8. Find the height (frequency density) of its bar.

A teacher plots a scatter graph of hours revised ($x$) against test mark ($y$) for a class. The points show that students who revised longer generally scored higher.(a) Describe the type of correlation shown.(b) The line of best fit passes through $(2, 40)$ and $(8, 76)$. Find the equation of the line of best fit.(c) Use your equation to estimate the mark of a student who revised for 5 hours.(d) Explain why the line should not be used to predict the mark of a student who revised for 20 hours.

80 students sat an exam. Marks: $0 < m \leq 20$ (4 students), $20 < m \leq 40$ (16), $40 < m \leq 60$ (30), $60 < m \leq 80$ (22), $80 < m \leq 100$ (8).(a) Estimate the median mark.(b) The top 25 percent of students are awarded a distinction. Estimate the lowest mark needed for a distinction.(c) A student claims the highest mark was 100. Explain whether the data supports this claim.